1(k) = A+ /2 22" +/2 2?(/2)" i=0 i=0 = A – 1/½(1 – 2*) – 6[(/2k² + k + 3/2)(½)* – 3/2)] ok (21.2

Q: 1. Use the Nth-Term Test to examine the divergence of: n n+1 n=1

A: Follow the steps and just remember the form of the nth tems test.

Q: 2n2 +n+2 ii. Use the result in (i) to test for convergence = 1 5n3 + 3n

A:

Q: 2. Find the interval of convergence of the series (n + 2)(x + 3)²n+2 2n

A: Here an=n+2x+32n+22n. The series converges if limn→∞an+1an<1

Q: - Find the interval of convergent for : 2n 2 2n! n=0

A:

Q: 3. For what values of x , does the series, 1-«-4)+ (* - 4)° --4). .... converge ?Find the ........…

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Q: (7) Express the function h(x) = -1 tan(2x) as a power series. Show your work. Hint: tan(2x) = |…

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Q: 1. Find the radius of convergence of (-1)" n! (3x + 1)" n=1

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Q: 6. Find the radius of convergence and the interval of convergence for E-0¹ (x-2)".

A: 6. The given power series is     ∑n=0∞12nx-2n We need to find the radius of convergence and the…

Q: 3. Use secant method to determine a root of f(x) = 4x³-16x2 + 17x-4 with initial guesses of x.1 = 2…

A: Given fx=4x3-16x2+17x-4 and x-1=2, x0=4

Q: Expand (2+ value of (1.9975)6 up to four decimal places. X\ 6 up to r³ in ascending power of r. Find…

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Q: The Integral Test enables us to bound the error approximation of the series n=1 n7/2 by the partial…

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Q: Q2:Expand using Maclourin series (1 - x 1-x² 2 ln(1 + x4) )? -

A: As per our guideline we are supposed to answer only one question of  multiple type of questions.…

Q: Find the interval of convergence of the series. Σ (x-1)n (5n)! n=1 -119 sxs 121 xS2 -00 <x< 00 0sxs2

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Q: (A) Verify that Jp+1(x) + 2½(x) – Jp-1(x) = 0 Tip: Compare the series of Jp+1(x) – Jp-1(x) and –…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Find a series solution for у" -ху %3D 0 around the point xo = -2

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Q: Find the interval of convergence of the series. (x-1) 5n+ 4 n=0

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Q: 10. It has been lo ponents produced in a certain factory are de hundred is drawn from each day's…

A: A random sample of size one hundred is drawn; n=100 1% of electronic components are defective;…

Q: 2) Determine the interval and radius of convergence of 2 '(x+5)** (2n +1)! 34n-1 n=0

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Q: ii. Investigate convergence or divergence of 2n + 100 3n +1). n=2

A: Given series is  ∑n=2∞-1n2n+1003n+1n

Q: What is the upper sum for f(x)=17−x2 on [3,4] using four subintervals? Round to the nearest…

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Q: (-1)"(х + 3)" Σ n2n n=1

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Q: Find the interval of convergence of the series. (x - 2)2n Σ 36 n=0 1<x < 3 -4 < x < 8 X < 8 -8 < x <…

A: Given: ∑n=0∞x-22n36n

Q: Consider the given ODE. You should be able to generate two Power Series Solutions for it. However,…

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Q: 9. Estimate the value of the convergent series 8 k=1 (-1)^² k! + 2k with an absolute error less than…

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Q: What is the function represented by the power series from k=0 to infinity of ((-1)^k*x^(k+1))/4^k?

A: Power series

Q: Discuss the three possibilities for the radius of convergence of a Taylor series.

A: If there exists a non negative real number 'r' (I.e., r ≥ 0) such that,  (i) the power series…

Q: Write power series of f(x) = 3 about x = 0. %3D 1- 4.r

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Q: Σ Why can't the integral test be used for the series K! K= 0 The function is not decreasing for all…

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Q: التاريخ الموضوع @/ using the integration test the series n³+n $ for apart Lin= √² +21² +2 A true…

A: Please see the attachment  Series is divergent.

Q: 2k と(+ 1) converges. Use the integral test to determine whether k-1

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Q: What is the function represented by the power series from k=0 to infinity of (-1)^k(x^k)/(3^k)?

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Q: [MO22] Express as a single power series form: > (n – 2)an+1(2x – 3)*1 +) an-1(2x – 3)"-1 n=0 n=2

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Q: Find the interval of convergence of the series (–1)"(x+3)*+1 п(п + 1) n=1

A:

Q: If 2 Cnx" is convergent when x=2 and divergent when x=-3, then 2 Cn is n=0 n =0 convergent. O…

A: Consider the given information: The series ∑n=0∞Cnxn is convergent when x=2 and divergent when x=-3.…

Q: Represent the function 5 ln(4-x) as a power series (Maclaurin series) of:

A: See the details solution below

Q: 6. Express the power series: >(-3)"(x)"-1 n=0 As a function. Then find its radius and interval of…

A: We can calculate radius of convergence by ratio test and then find interval of convergence

Q: 2. [MO22] Express as a single power series form: (п — 2)аn+1(2х - 3)"+1 + ->, ап-1(2х — 3)"-1 n=0…

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Q: Find the interval of convergence of the series. (x-5) 5n+1 n=0

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Q: 2n2 +n+2 Σ ii. Use the result in (i) to test for convergence = 1 5n3 + 3n

A:

Q: 2. Use the Binomial Theorem for the expansion of the function as a power ser: S(x) = V1+ 3x²

A:

Q: 2. Write the formula for finding a root of f(x) = - x³ –- cos (x), where x is a real positive…

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Q: Find a sequence X, such that it does not converge to any real number, but Y, does converge to some…

A: Consider the sequence Xn=(-1)n. Then Xn={-1,1,-1,1,-1,1,-1,1,...}. So, Xn does not converges to any…

Q: (1+x)-3=1-3x+6x2-10x3........ with  ex= 1+x +x2/2 +x3/6............

A: Here we use the D'Almbert ratio test.

Q: Express F in terms of functions that you know the power series expansion for

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Q: 8. 3n2 -n 6n2 + 7 n=1

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Q: If 2 Cnx" is convergent when x=2 and divergent when x--3, then 2 c,5" n = 0 is n= 0 divergent. O…

A: this is inconclusive because if it converges for x=2 than  converges only the values less than 2 but…

Q: [MO22] Express as a single power series form: > (n – 2)an+1(2x – 3)n+1+ > an-1(2x – 3)"-1 n=0 n=2

A:

Q: Can we use two ways to show 1 Σ n² +5n+6 n = 0 to n = infinity, convergent or divergent ? Say, 1)…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.